Timestamp inconsistency and shift detection for synchrophasor data based on correlation between relative phase angle and frequency

ABSTRACT

A method includes performing by a processor: receiving a plurality of synchrophasor measurements of a power system signal associated with a time interval from a phasor measurement unit (PMU), each of the plurality of synchrophasor measurements including a phase angle, frequency value, and a timestamp associated with the synchrophasor measurement, determining a plurality of relative phase angles based on the plurality of phase angles, determining a correlation coefficient between the plurality of relative phase angles and a plurality of corresponding frequency values of the power system signal, and detecting an error in the plurality of timestamps based on the correlation coefficient; estimating the error in the plurality of timestamps based on the plurality of relative phase angles and the plurality of corresponding frequency values.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under contract numberNSF EEC1041877 awarded by the National Science Foundation. Thegovernment has certain rights in the invention.

BACKGROUND

The present disclosure relates to power systems, and, in particular, tomonitoring, operation, and control of power systems.

Phasor Measurement Units (PMUs) are devices that are used to estimatethe magnitude and phase angle of the voltage or current in a powersystem using a common time source for synchronization. PMUs areincreasingly deployed in power systems in to provide synchronizedmeasurements for system situational awareness and observation ofbehavioral dynamics. The PMUs may be placed in various locations withina power system including the main power grid, the distribution grid,and/or consumer locations. PMUs may be used to collect samples from awaveform in quick succession and to reconstruct the phasor quantity,which is made up of an angle measurement and a magnitude measurementknown as a synchrophasor measurement.

The frequency of a power system may be affected by the balance betweenpower generation and load consumption. Power consumption and/or powergeneration may both vary, which may result in the two rarely beingprecisely in balance. During normal operation, changes in frequency maybe controlled by ancillary services that provide continuous, automaticfrequency control through automatic generator control (AGC). However,severe electromechanical disturbances, such as generation trip and loadreduction, can cause significant drops and/or increases in systemfrequency and may influence the dynamic behavior of a power grid.Therefore, it is generally desirable to prevent and/or reduce largedeviations of the power system frequency from the nominal frequencyduring large disturbances so as to improve the operational stability ofpower systems. The synchrophasor measurements from the PMUs may be usedto detect events in the power system that may cause deviations in powersystem frequency from the nominal frequency range or other potentialproblems or malfunctions in the power system.

A power system may use the Global Positioning System (GPS) to alignsynchrophasor data that has been collected from various PMUs foranalysis. A Phasor Data Concentrator (PDC) may rely on timestampsattached to each synchrophasor measurement. The PMUs receive the timeinformation from the GPS and include this information with thesynchrophasor measurement when transmitting the measurement to the PDC.Normally the synchrophasor measurements are timestamped with a margin oferror of approximately 100 nanoseconds under good GPS receptionconditions. However, phasor calculation may use data from a time windowof one to two 60 Hz cycles and different vendors may use differentapproaches to assign the calculated value from the beginning to the endof the time window. This inconsistency may introduce timesynchronization errors. Although Pulse Per Second (PPS) from a GPSreceiver can be accurate to within a few nanoseconds, the GPS timeserial output may have a much larger latency, which can be as large as ahalf-second. Improper handling of the latency may enlarge the timesynchronization errors. Other uncontrollable and unpredictable factors,such as temporal hardware malfunctions may result in imperfectsynchronization and time skew between the PMU synchrophasor measurementseven after the PMUs have been calibrated. In addition, events such asleap years or GPS rollover, i.e., the reset in the field used to holdthe week number from its maximum number periodically to zero, may alsocause synchronization errors. The timestamp time shift or skew in thesynchrophasor measurement data may adversely affect power systemoperations that may rely on a high level of synchrophasor measurementsynchronization, such as, power system protection, fault location,oscillation detection, and event triangulation. Because the timestamptime shift in the synchrophasor measurement data from the PMUs may berelatively small, e.g., less than one second, the shift may be difficultto detect.

SUMMARY

In some embodiments of the inventive concept, a method comprisesperforming by a processor: receiving a plurality of synchrophasormeasurements of a power system signal associated with a time intervalfrom a phasor measurement unit (PMU), each of the plurality ofsynchrophasor measurements including a phase angle, frequency value, anda timestamp associated with the synchrophasor measurement, determining aplurality of relative phase angles based on the plurality of phaseangles, determining a correlation coefficient between the plurality ofrelative phase angles and a plurality of corresponding frequency valuesof the power system signal, and detecting an error in the plurality oftimestamps based on the correlation coefficient; estimating the error inthe plurality of timestamps based on the plurality of relative phaseangles and the plurality of corresponding frequency values.

In other embodiments, the method further comprises adjusting theplurality of timestamps of the plurality of synchrophasor measurementsreceived from the PMU based on the error.

In still other embodiments, the plurality of synchrophasor measurementsis a first plurality of synchrophasor measurements, the plurality ofphase angles is a first plurality of phase angles, the plurality oftimestamps is a first plurality of timestamps, and the time interval isa first time interval, the method further comprising: receiving a secondplurality of synchrophasor measurements of the power system signalassociated with a second time interval from the PMU, each of the secondplurality of synchrophasor measurements including a second phase angleand a second timestamp associated with the synchrophasor measurement andadjusting the second plurality of timestamps associated with the secondplurality of synchrophasor measurements received from the PMU based onthe error.

In still other embodiments, the method further comprises performing anadministrative operation on the power system based on the plurality ofsynchrophasor measurements having the plurality of timestamps,respectively, that have been adjusted.

In still other embodiments, determining the plurality of relative phaseangles based on the plurality of phase angles comprises: subtracting apower system average phase angle or a phase angle of a reference PMUfrom each of the plurality of phase angles to obtain the plurality ofrelative phase angles.

In still other embodiments, determining the correlation coefficientbetween the plurality of relative phase angles and the plurality ofcorresponding frequency values of the power system signal comprises:determining a covariance between the plurality of relative phase anglesand the plurality of corresponding frequency values, determining astandard deviation of the plurality of relative phase angles,determining a standard deviation of the plurality of correspondingfrequency values, and dividing the covariance by a product of thestandard deviation of the plurality of relative phase angles and thestandard deviation of the plurality of corresponding frequency values.

In still other embodiments, detecting the error in the plurality oftimestamps based on the correlation coefficient comprises: comparing thecorrelation coefficient to a threshold and detecting the error in theplurality of timestamps based on a difference between the correlationcoefficient and the threshold.

In still other embodiments, estimating the error in the plurality oftimestamps based on the plurality of relative phase angles and theplurality of corresponding frequency values comprises: determining arelative phase angle difference between a maximum relative phase anglevalue of the plurality of relative phase angles and a minimum relativephase angle value of the plurality of relative phase angles, determininga frequency difference between the frequency value at a time of amaximum relative phase angle and the frequency value at a time of aminimum relative phase angle, and estimating the error in the pluralityof timestamps based on the .relative phase angle difference divided by aproduct of the frequency difference and 2π.

In still other embodiments, the plurality of synchrophasor measurementsis a first plurality of synchrophasor measurements, the plurality ofphase angles is a first plurality of phase angles, the plurality oftimestamps is a first plurality of timestamps, the time interval is afirst time interval, the plurality of relative phase angles is a firstplurality of relative phase angles, and the correlation coefficient is afirst correlation coefficient, the method further comprising: receivinga second plurality of synchrophasor measurements of the power systemsignal associated with a second time interval from the PMU, each of thesecond plurality of synchrophasor measurements including a second phaseangle and a second timestamp associated with the synchrophasormeasurement, determining a second plurality of relative phase anglesbased on the second plurality of phase angles, determining a secondcorrelation coefficient between the second plurality of relative phaseangles and a second plurality of corresponding frequency values of thepower system signal, and determining an average of the first correlationcoefficient and the second correlation coefficient.

In still other embodiments, detecting the error in the first pluralityof timestamps based on the correlation coefficient comprises: detectingthe error in the first plurality of timestamps and the second pluralityof timestamps based on the average of the first correlation coefficientand the second correlation coefficient. Estimating the error in thefirst plurality of timestamps based on the first plurality of relativephase angles and the first plurality of corresponding frequency valuescomprises: estimating the error in the first plurality of timestamps andthe second plurality of timestamps based on the first plurality ofrelative phase angles, the second plurality of relative phase angles,the first plurality of corresponding frequency values, and the secondplurality of corresponding frequency values.

In some embodiments of the inventive concept, a system comprises aprocessor and a memory coupled to the processor and comprising computerreadable program code embodied in the memory that is executable by theprocessor to perform operations comprising: receiving a plurality ofsynchrophasor measurements of a power system signal associated with atime interval from a phasor measurement unit (PMU), each of theplurality of synchrophasor measurements including a phase angle,frequency value, and a timestamp associated with the synchrophasormeasurement, determining a plurality of relative phase angles based onthe plurality of phase angles, determining a correlation coefficientbetween the plurality of relative phase angles and a plurality ofcorresponding frequency values of the power system signal, detecting anerror in the plurality of timestamps based on the correlationcoefficient, and estimating the error in the plurality of timestampsbased on the plurality of relative phase angles and the plurality ofcorresponding frequency values.

In further embodiments, the operations further comprise: adjusting theplurality of timestamps of the plurality of synchrophasor measurementsreceived from the PMU based on the error.

In still further embodiments, determining the correlation coefficientbetween the plurality of relative phase angles and the plurality ofcorresponding frequency values of the power system signal comprises:determining a covariance between the plurality of relative phase anglesand the plurality of corresponding frequency values, determining astandard deviation of the plurality of relative phase angles,determining a standard deviation of the plurality of correspondingfrequency values, and dividing the covariance by a product of thestandard deviation of the plurality of relative phase angles and thestandard deviation of the plurality of corresponding frequency values.

In still further embodiments, detecting the error in the plurality oftimestamps based on the correlation coefficient comprises: comparing thecorrelation coefficient to a threshold and detecting the error in theplurality of timestamps based on a difference between the correlationcoefficient and the threshold.

In still further embodiments, estimating the error in the plurality oftimestamps based on the plurality of relative phase angles and theplurality of corresponding frequency values comprises: determining arelative phase angle difference between a maximum relative phase anglevalue of the plurality of relative phase angles and a minimum relativephase angle value of the plurality of relative phase angles, determininga frequency difference between the frequency value at a time of amaximum relative phase angle and the frequency value at a time of aminimum relative phase angle, and estimating the error in the pluralityof timestamps based on the .relative phase angle difference divided by aproduct of the frequency difference and 2π.

In some embodiments of the inventive concept, a computer program productcomprises a tangible computer readable storage medium comprisingcomputer readable program code embodied in the medium that is executableby a processor to perform operations comprising: receiving a pluralityof synchrophasor measurements of a power system signal associated with atime interval from a phasor measurement unit (PMU), each of theplurality of synchrophasor measurements including a phase angle,frequency value, and a timestamp associated with the synchrophasormeasurement, determining a plurality of relative phase angles based onthe plurality of phase angles, determining a correlation coefficientbetween the plurality of relative phase angles and a plurality ofcorresponding frequency values of the power system signal, detecting anerror in the plurality of timestamps based on the correlationcoefficient, and estimating the error in the plurality of timestampsbased on the plurality of relative phase angles and the plurality ofcorresponding frequency values.

In other embodiments, the operations further comprise: adjusting theplurality of timestamps of the plurality of synchrophasor measurementsreceived from the PMU based on the error.

In still other embodiments, determining the correlation coefficientbetween the plurality of relative phase angles and the plurality ofcorresponding frequency values of the power system signal comprises:determining a covariance between the plurality of relative phase anglesand the plurality of corresponding frequency values, determining astandard deviation of the plurality of relative phase angles,determining a standard deviation of the plurality of correspondingfrequency values, and dividing the covariance by a product of thestandard deviation of the plurality of relative phase angles and thestandard deviation of the plurality of corresponding frequency values.

In still other embodiments, detecting the error in the plurality oftimestamps based on the correlation coefficient comprises: comparing thecorrelation coefficient to a threshold and detecting the error in theplurality of timestamps based on a difference between the correlationcoefficient and the threshold.

In still other embodiments, estimating the error in the plurality oftimestamps based on the plurality of relative phase angles and theplurality of corresponding frequency values comprises: determining arelative phase angle difference between a maximum relative phase anglevalue of the plurality of relative phase angles and a minimum relativephase angle value of the plurality of relative phase angles, determininga frequency difference between the frequency value at a time of amaximum relative phase angle and the frequency value at a time of aminimum relative phase angle, and estimating the error in the pluralityof timestamps based on the .relative phase angle difference divided by aproduct of the frequency difference and 2π.

Other methods, systems, articles of manufacture, and/or computer programproducts, according to embodiments of the inventive concept, will be orbecome apparent to one with skill in the art upon review of thefollowing drawings and detailed description. It is intended that allsuch additional systems, methods, articles of manufacture, and/orcomputer program products be included within this description, be withinthe scope of the present inventive concept, and be protected by theaccompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features of embodiments will be more readily understood from thefollowing detailed description of specific embodiments thereof when readin conjunction with the accompanying drawings, in which:

FIG. 1 is a block diagram that illustrates a power distribution networkincluding a synchrophasor measurement timestamp time shift detectioncapability in accordance with some embodiments of the inventive concept;

FIG. 2 illustrates a data processing system that may be used toimplement a Distribution Management System (DMS) processor associatedwith a power system of FIG. 1 in accordance with some embodiments of theinventive concept;

FIG. 3 is a block diagram that illustrates a software/hardwarearchitecture for use in a DMS processor for detecting synchrophasormeasurement timestamp time shifts in a power system in accordance withsome embodiments of the inventive concept;

FIGS. 4-8 are flowcharts that illustrate operations for detectingsynchrophasor measurement timestamp time shifts in a power system inaccordance with some embodiments of the inventive concept;

FIGS. 9A-9C are graphical representations illustrating the correlationbetween relative phase angle and frequency when synchrophasormeasurements are timestamp time shifted in accordance with someembodiments of the inventive concept; and

FIGS. 10A and 10B are graphical representations illustrating thecorrelation between relative phase angle and frequency whensynchrophasor measurements are timestamped shifted based on experimentaldata obtained from a power system.

DETAILED DESCRIPTION

In the following detailed description, numerous specific details are setforth to provide a thorough understanding of embodiments of the presentdisclosure. However, it will be understood by those skilled in the artthat the present invention may be practiced without these specificdetails. In some instances, well-known methods, procedures, componentsand circuits have not been described in detail so as not to obscure thepresent disclosure. It is intended that all embodiments disclosed hereincan be implemented separately or combined in any way and/or combination.Aspects described with respect to one embodiment may be incorporated indifferent embodiments although not specifically described relativethereto. That is, all embodiments and/or features of any embodiments canbe combined in any way and/or combination.

As used herein, the term “data processing facility” includes, but it isnot limited to, a hardware element, firmware component, and/or softwarecomponent. A data processing system may be configured with one or moredata processing facilities.

As used herein, the term “real-time” may mean an operation is performedwithout inserting any artificial scheduling or processing delays.

Some embodiments of the inventive concept may stem from a realizationthat that when a time shift or skew occurs in timestamps for PhasorMeasurement Unit (PMU) synchrophasor measurement data, the relativephase angle and frequency of the power signal obtained through thesynchrophasor data are correlated. In a relative short time interval,the relative phase angle, which varies with power flow between areas,may be considered a stochastic process. The time shift or skew in thetimestamps of the synchrophasor measurement data may introduce acomponent into the relative phase angle that has a linear relationshipwith frequency. This similarity or correlation between the relativephase angle and frequency may be used as an indicator for detectingwhether a time shift or skew has occurred in the timestamps for thesynchrophasor measurement data generated by a PMU. In other words, ifthe relative phase angle is determined to be similar or have a generallyhigh correlation with frequency, then the synchrophasor measurement datagenerated by a PMU may include time shifted timestamps.

Referring to FIG. 1, a power system distribution network 100 including asynchrophasor measurement timestamp time shift detection capability, inaccordance with some embodiments of the inventive concept, comprises amain power grid 102, which is typically operated by a public or privateutility, and which provides power to various power consumers 104 a, 104b, 104 c, 104 d, 104 e, and 104 f. The electrical power generators 106a, 106 b, and 106 c are typically located near a fuel source, at a damsite, and/or at a site often remote from heavily populated areas. Thepower generators 106 a, 106 b, and 106 c may be nuclear reactors, coalburning plants, hydroelectric plants, and/or other suitable facility forgenerating bulk electrical power. The power output from the powergenerators 106, 106 b, and 106 c is carried via a transmission grid ortransmission network over potentially long distances at relatively highvoltage levels. A distribution grid 110 may comprise multiplesubstations 116 a, 116 b, 116 c, which receive the power from thetransmission grid 108 and step the power down to a lower voltage levelfor further distribution. A feeder network 112 distributes the powerfrom the distribution grid 110 substations 116 a, 116 b, 116 c to thepower consumers 104 a, 104 b, 104 c, 104 d, 104 e, and 104 f. The powersubstations 116 a, 116 b, 116 c in the distribution grid 110 may stepdown the voltage level when providing the power to the power consumers104 a, 104 b, 104 c, 104 d, 104 e, and 104 f through the feeder network112.

As shown in FIG. 1, the power consumers 104 a, 104 b, 104 c, 104 d, 104e, and 104 f may include a variety of types of facilities including, butnot limited to, a warehouse 104 a, a multi-building office complex 104b, a factory 104 c, and residential homes 104 d, 104 e, and 104 f. Afeeder circuit may connect a single facility to the main power grid 102as in the case of the factory 104 c or multiple facilities to the mainpower grid 102 as in the case of the warehouse 104 a and office complex104 b and also residential homes 104 d, 104 e, and 104 f. Although onlysix power consumers are shown in FIG. 1, it will be understood that afeeder network 112 may service hundreds or thousands of power consumers.

The power distribution network 100 further comprises a DistributionManagement System (DMS) 114, which may monitor and control thegeneration and distribution of power via the main power grid 102. TheDMS 114 may comprise a collection of processors and/or servers operatingin various portions of the main power grid 102 to enable operatingpersonnel to monitor and control the main power grid 102. The DMS 114may further include other monitoring and/or management systems for usein supervising the main power grid 102. One such system is known as theSupervisory Control and Data Acquisition (SCADA) system, which is acontrol system architecture that uses computers, networked datacommunications, and graphical user interfaces for high-level processsupervisory management of the main power grid. The DMS 114 may furtherinclude a phasor data concentrator module that is configured to managethe reception and processing of synchrophasor measurements from the PMUs118 a, 118 b, and 118 c. The phasor data concentrator module maycooperate with other supervisory, monitoring, and control modules,systems, and/or capabilities provided via the DMS 114

According to some embodiments of the inventive concept, PMUs 118 a, 118b, and 118 c may be located at the substations 116 a, 116 b, and 116 c,respectively. PMUs measure current and voltage by amplitude and phase atselected stations of the distribution grid 110. Using Global PositioningSystem (GPS) information, for example, high-precision timesynchronization may allow comparing measured values (synchrophasors)from different substations distant to each other and drawing conclusionsregarding the system state and dynamic events, such as power swingconditions. The PMUs 118 a, 118 b, 118 c may determine current andvoltage phasors, frequency, and rate of change of frequency and providethese measurements with time stamps for transmittal to the DMS 114 foranalysis. The PMUs 118 a, 118 b, 118 c may communicate with the DMS 114over the network 120. The network 120 may be a global network, such asthe Internet or other publicly accessible network. Various elements ofthe network 120 may be interconnected by a wide area network, a localarea network, an Intranet, and/or other private network, which may notbe accessible by the general public. Thus, the communication network 120may represent a combination of public and private networks or a virtualprivate network (VPN). The network 120 may be a wireless network, awireline network, or may be a combination of both wireless and wirelinenetworks. Although the PMUs 118 a, 118 b, and 118 c are shown as beinglocated in the substations 116 a, 116 b, and 116 c, it will beunderstood that the PMUs may be located in other locations within thedistribution grid 110, within the main power grid 102, or even atconsumer locations 104 a, 104 b, 104 c, 104 d, 104 e, and 104 f, suchas, for example, in proximity to wall outlets or other power accesspoints.

Although FIG. 1 illustrates an exemplary a power distribution network100 including a synchrophasor measurement timestamp time shift detectioncapability, it will be understood that embodiments of the inventiveconcept are not limited to such configurations, but are intended toencompass any configuration capable of carrying out the operationsdescribed herein.

Referring now to FIG. 2, a data processing system 200 that may be usedto implement the DMS 114 processor of FIG. 1, in accordance with someembodiments of the inventive concept, comprises input device(s) 202,such as a keyboard or keypad, a display 204, and a memory 206 thatcommunicate with a processor 208. The data processing system 200 mayfurther include a storage system 210, a speaker 212, and an input/output(I/O) data port(s) 214 that also communicate with the processor 208. Thestorage system 210 may include removable and/or fixed media, such asfloppy disks, ZIP drives, hard disks, or the like, as well as virtualstorage, such as a RAMDISK. The I/O data port(s) 214 may be used totransfer information between the data processing system 200 and anothercomputer system or a network (e.g., the Internet). These components maybe conventional components, such as those used in many conventionalcomputing devices, and their functionality, with respect to conventionaloperations, is generally known to those skilled in the art. The memory206 may be configured with sustained oscillation detection module 216that may provide functionality that may include, but is not limited to,detecting time shifts in timestamps for synchrophasor measurementsobtained from one or more PMUs 118 a, 118 b, and 118 c in accordancewith some embodiments of the inventive concept.

FIG. 3 illustrates a processor 300 and memory 305 that may be used inembodiments of data processing systems, such as the DMS 114 processor ofFIG. 1 and the data processing system 200 of FIG. 2, respectively, fordetecting synchrophasor measurement timestamp time shifts, in accordancewith some embodiments of the inventive concept. The processor 300communicates with the memory 305 via an address/data bus 310. Theprocessor 300 may be, for example, a commercially available or custommicroprocessor. The memory 305 is representative of the one or morememory devices containing the software and data used for detectingsynchrophasor measurement timestamp time shifts in accordance with someembodiments of the inventive concept. The memory 305 may include, but isnot limited to, the following types of devices: cache, ROM, PROM, EPROM,EEPROM, flash, SRAM, and DRAM.

As shown in FIG. 3, the memory 305 may contain two or more categories ofsoftware and/or data: an operating system 315 and a timestamp time shiftdetection module 320. In particular, the operating system 315 may managethe data processing system's software and/or hardware resources and maycoordinate execution of programs by the processor 300. The timestamptime shift detection module 320 may comprise a PMU data collectionmodule 325, a relative phase angle generation module 330, a correlationanalysis module 335, a timestamp error estimation module 340, an alertmodule 345, a data module 350, and a communication module 355.

The PMU data collection module 325 may be configured to receive measuredinformation, such as, for example, time-stamped power systemsynchrophasor measurements from the PMUs 118 a, 118 b, and 118 c in thedistribution grid 110. Each of the synchrophasor measurements of a powersystem signal may include a phase angle, frequency value, and atimestamp associated with the synchrophasor measurement.

The relative phase angle generation module 330 may be configured todetermine relative phase angles from the phase angle data in thesynchrophasor measurements obtained from the PMUs 118 a, 118 b, and 118c. The real phase angle of the complex voltage/current signal changes atthe rate of 2πf while the reported phase angle from the PMUs 118 a, 118b, and 118 c is the instant angle value at the reporting time, where fis the frequency of the measured signal. The deviation of phase angle ΔAcan be derived as EQ. (1), where f_(N) is the nominal frequency, e.g. 50Hz or 60 Hz.ΔA=2π∫(f−f _(N))·dt  (1)

Relative phase angle A_(rel) is defined as Eq. (2),A _(rel)(T)=A(T)−A _(ref)(T)  (2)

where A is the measured phase angle and A_(ref) is a reference phaseangle, which, in some embodiments, may be a power system average phaseangle.

The relative phase angle generation module may be further configured todetermine the variation of relative phase angle during a defined timeinterval. Combining EQ. 1 and 2 and defining Δt as a PMU's 118 a, 118 b,and 118 c reporting interval, the variation of relative phase angleduring the interval Δt can be derived:

$\begin{matrix}\begin{matrix}{{\Delta\;{A_{rel}(T)}} = {{\Delta\;{A(T)}} - {\Delta\;{A_{ref}(T)}}}} \\{= {2\pi{\int_{T - {\Delta\; t}}^{T}{\left( {f - f_{ref}} \right) \cdot {dt}}}}} \\{\overset{\Delta}{=}{2{\pi \cdot \left( {f - f_{ref}} \right) \cdot \Delta}\; t}}\end{matrix} & (3)\end{matrix}$

Because relative phase angle varies with power flow among areas, therelative phase angle and its variation may also be considered astochastic process. For example, when multiple PMUs 118 a, 118 b, and118 c are deployed in a synchronized power grid, and one individual PMU118 a, 118 b, and 118 c has timestamp time shift in its synchrophasormeasurements, the inaccurate time T′ may be defined as set forth in EQ.(4):T′=T+τ  (4)where T is the accurate time and τ is the time shift value.

Based on the time shifted synchrophasor measurement, the correspondingrelative phase angle variation can be calculated as set forth inEquations (5) and (6)″

$\begin{matrix}\begin{matrix}{{\Delta\;{A_{rel}\left( T^{\prime} \right)}} = {2{\pi \cdot \left\lbrack {{f\left( T^{\prime} \right)} - {f_{ref}(T)}} \right\rbrack \cdot \Delta}\; t}} \\{= {2{\pi \cdot \left\lbrack {{f(T)} + {\Delta\;{f_{\tau}(T)}} - {f_{ref}(T)}} \right\rbrack \cdot \Delta}\; t}} \\{= {{\Delta\;{A_{ref}(T)}} + {2{\pi \cdot \Delta}\;{{f_{\tau}(T)} \cdot \Delta}\; t}}}\end{matrix} & (5)\end{matrix}$where Δf_(τ)(T) is frequency variation between time T′ and T. Then Eq.(6) can be derived from the integral of Eq. (5):

$\begin{matrix}{{A_{rel}\left( T^{\prime} \right)} \approx {{A_{rel}(T)} + \underset{\underset{D}{︸}}{{f{(T) \cdot 2}{\pi \cdot \tau}} + C}}} & (6)\end{matrix}$where A_(rel)(T′) is the relative phase angle with a time shift,A_(rel)(T) is the true relative phase angle, and C is a constant.

As described above, A_(rel)(T) may be considered as a stochasticcomponent. However, the remaining part of the right side “D” of EQ. (6)is a component that is linear with respect to frequency. Therefor a timeshift in the timestamps associated with synchrophasor measurements froma PMU 118 a, 118 b, and 118 c may be detected when a similaritycomponent that is linear with respect to frequency is found inA_(rel)(T′). In other words, when a correlation, such as a linearrelationship, is found between relative phase angles associated withsynchrophasor measurements and the frequency of the power signal fromwhich the measurements were derived over a time interval, then thiscorrelation may be indicative of a time shift in the timestampsassociated with the synchrophasor measurements.

The correlation analysis module 335 may be configured to quantify thesimilarity or relationship between the relative phase angles associatedwith the synchrophasor measurements and the frequency of the powersignal. In some embodiments, this quantification may take the form of adetermination of a correlation coefficient between the relative phaseangle A_(rel) and frequency f as set forth in EQ. 7:

$\begin{matrix}{\rho_{A_{rel},f} = \frac{{cov}\left( {A_{rel},f} \right)}{\sigma_{A_{rel}}\sigma_{f}}} & (7)\end{matrix}$where cov(.) and σ represent the covariance and standard deviationfunctions, respectively.

In some embodiments, when ρ_(A) _(rel) _(,f) exceeds a threshold ε, atime shift in the timestamps associated with synchrophasor measurementsobtained from a PMU 118 a, 118 b, and 118 c may be detected, where ε maybe empirically selected via simulation study using historical ambientsynchrophasor data with the introduction of artificial time shifts inthe synchrophasor measurement data.

The timestamp error estimation module 340 may be configured to estimatethe error, i.e., the amount of shift, in the time shifted timestamps ofthe synchrophasor measurements. In some embodiments, once a timestamptime shifted event for synchrophasor measurements is detected, the timeerror z can be estimated as set forth in EQ. (8) as follows

$\begin{matrix}{\tau \approx \frac{\Delta A_{rel}}{2{\pi \cdot \Delta}\; f}} & (8)\end{matrix}$

The synchrophasor measurements obtained from the PMU 118 a, 118 b, and118 c may have their timestamps adjusted based on the determined errorso as to improve synchronization with the actual reference clock signal,e.g., GPS clock, and/or other PMUs 118 a, 118 b, and 118 c. Thesetimestamp adjustments may be made on the synchrophasor measurements usedto determine the error as well as future synchrophasor measurementsreceived from the PMU 118 a, 118 b, and 118 c until a new timestamp timeshift detection analysis is performed to estimate a new error, e.g.,timestamp time shift, value.

The alert module 345 may be configured to generate an alert ornotification to the appropriate supervisory authority for the main powergrid 102 by way of the DMS 114. The alert or notification may furthertrigger the automated or manual performance of an administrativeoperation on the power system. Such operations may include, but are notlimited to, power system protection operations, power system faultlocation operations, power system oscillation detection operations, andpower system event triangulation operations.

The data module 350 may represent the power system synchrophasormeasurements from the PMUs 118 a, 118 b, and 118 c and received by thePMU data collection module 325, the threshold used by the correlationanalysis module 335, and other data structures used by the timestamptime shift detection module 320 for detecting synchrophasor measurementtimestamp time shifts in a power system in accordance with someembodiments of the inventive concept.

The communication module 355 may be configured to facilitatecommunication between the DMS 114 processor and the PMUs 118 a, 118 b,and 118 c of FIG. 1 over the network 120 and to facilitate communicationof an alert or notification to the appropriate supervisory authorityover one or more wired or wireless networks upon detection of atimestamp time shift event in the synchrophasor measurement dataallowing for the option to correct the timestamp time shift error asdescribed above with respect to the timestamp error estimation module340. In some embodiments, the correction of the time shift errors in thesynchrophasor data may be performed automatically in response toestimating the error.

Although FIG. 3 illustrates hardware/software architectures that may beused in data processing systems, such as the DMS 114 processor of FIG. 1and the data processing system 200 of FIG. 2, respectively, fordetecting synchrophasor measurement timestamp time shifts, in accordancewith some embodiments of the inventive concept it will be understoodthat the present invention is not limited to such a configuration but isintended to encompass any configuration capable of carrying outoperations described herein.

Computer program code for carrying out operations of data processingsystems discussed above with respect to FIGS. 1-3 may be written in ahigh-level programming language, such as Python, Java, C, and/or C++,for development convenience. In addition, computer program code forcarrying out operations of the present invention may also be written inother programming languages, such as, but not limited to, interpretedlanguages. Some modules or routines may be written in assembly languageor even micro-code to enhance performance and/or memory usage. It willbe further appreciated that the functionality of any or all of theprogram modules may also be implemented using discrete hardwarecomponents, one or more application specific integrated circuits(ASICs), or a programmed digital signal processor or microcontroller.

Moreover, the functionality of the DMS 114 processor of FIG. 1, the dataprocessing system 200 of FIG. 2, and the hardware/software architectureof FIG. 3, may each be implemented as a single processor system, amulti-processor system, a multi-core processor system, or even a networkof stand-alone computer systems, in accordance with various embodimentsof the inventive concept. Each of these processor/computer systems maybe referred to as a “processor” or “data processing system.”

The data processing apparatus of FIGS. 1-3 may be used to facilitate thedetection of synchrophasor measurement timestamp time shifts in a powersystem, according to various embodiments described herein. Theseapparatus may be embodied as one or more enterprise, application,personal, pervasive and/or embedded computer systems and/or apparatusthat are operable to receive, transmit, process and store data using anysuitable combination of software, firmware and/or hardware and that maybe standalone or interconnected by any public and/or private, realand/or virtual, wired and/or wireless network including all or a portionof the global communication network known as the Internet, and mayinclude various types of tangible, non-transitory computer readablemedia. In particular, the memory 206 coupled to the processor 208 andthe memory 305 coupled to the processor 300 include computer readableprogram code that, when executed by the respective processors, causesthe respective processors to perform operations including one or more ofthe operations described herein with respect to FIGS. 4-8, 9A-9C, 10A,and 10B.

FIG. 4 is a flowchart that illustrates operations for detectingsynchrophasor measurement timestamp time shifts in a power system inaccordance with some embodiments of the inventive concept. Operationsbegin at block 400 where the PMU data collection module 325 receivessynchrophasor measurements where each of the synchrophasor measurementsincludes a phase angle, a frequency value, and a timestamp associatedwith the synchrophasor measurement from one of the PMUs 118 a, 118 b,and 118 c. The measurements may correspond to a measurement collectiontime interval, which may be, in some embodiments, about 200 seconds induration. It will be understood that while only three PMUs areillustrated in FIG. 1, fewer or more PMUs may be used in accordance withvarious embodiments of the inventive concept. At block 405, the relativephase angle generation module 330 determines the relative phase anglesbased on the phase angles included in the synchrophasor measurements. Insome embodiments, the relative phase angles may be determined bysubtracting a reference phase angle or a phase angle of a reference PMU,which, in some embodiments, may be a power system average phase angle,from the phase angles included in the synchrophasor measurements. Thecorrelation analysis module 335 quantifies a similarity between therelative phase angles and the corresponding frequency values of thepower system signal at block 410 by determining a correlationcoefficient between the relative phase angles and the correspondingfrequency values. The timestamp error estimation module 340 detects anerror, i.e., a time shift, in the timestamps of the PMU synchrophasormeasurements at block 415 based on the correlation coefficient. Forexample, in some embodiments, when the correlation coefficients exceedsa defined threshold where the greater the coefficient value, the higherthe correlation, then the timestamp error estimation module 340 detectsa time shift error in the synchrophasor timestamps. Otherwise, thecorrelation may be deemed to be insufficient to indicate a time shifterror in the synchrophasor measurements. The timestamp error estimationmodule 340 estimates the error based on the relative phase angles andthe corresponding frequency values of the power system signal at block420.

FIG. 5 is a flowchart that illustrates further operations for detectingsynchrophasor measurement timestamp time shifts in a power system inaccordance with some embodiments of the inventive concept. Operationsbegin at block 500 where the timestamp error estimation module 340adjusts the plurality of timestamps based on the estimated error. Thesetimestamp adjustments may be made on the synchrophasor measurements usedto determine the error and/or future synchrophasor measurements receivedfrom the PMU 118 a, 118 b, and 118 c until a new timestamp time shiftdetection analysis is performed to estimate a new error, e.g., timestamptime shift, value.

FIG. 6 is a flowchart that illustrates further operations for detectingsynchrophasor measurement timestamp time shifts in a power system inaccordance with some embodiments of the inventive concept. Operationsbegin at block 600 where the alert module 345 may trigger the automatedor manual performance of an administrative operation on the power systembased on the synchrophasor measurements with the adjusted, i.e., errorcorrected, timestamps. Such operations may include, but are not limitedto, power system protection operations, power system fault locationoperations, power system oscillation detection operations, and powersystem event triangulation operations.

FIG. 7 is a flowchart that illustrates further operations of block 415of FIG. 4 for determining the correlations coefficient according to someembodiments of the inventive concept. Operations begin at block 700where a covariance is determined between the relative phase angles ofthe synchrophasor measurements and the corresponding frequency values. Astandard deviation of the relative phase angles is determined at block705 and a standard deviation of the corresponding frequency values isdetermined at block 710. The covariance is divided by a product of thestandard deviation of the relative phase angles and the standarddeviation of the corresponding frequency values at block 715. Thus, theoperations of blocks 700, 705, 710, and 715 may be used to determine acorrelation coefficient as set forth above in EQ. 7 in accordance withsome embodiments of the inventive concept.

FIG. 8 is a flowchart that illustrates further operations of block 420of FIG. 4 for estimating the error in the timestamps of thesynchrophasor measurements obtained from one of the PMUs 118 a, 118 b,and 118 c. Operations begin at block 800 where a difference between amaximum relative phase angle value and a minimum relative phase anglevalue is determined as the relative phase angle difference. At block 805a difference between the frequency value at a time of a maximum relativephase angle and the frequency value at a time of a minimum relativephase angle is determined as the frequency difference. The error isestimated at block 810 based on the relative phase angle differencedivided by a product of the frequency difference and 2π. Thus, theoperations at blocks 800, 805, and 810 may be used to determine thesynchrophasor timestamp time shift error as set forth above in EQ. 8 inaccordance with some embodiments of the inventive concept.

The operations of FIG. 4 and FIG. 8 may be performed multiple times fordifferent time intervals to determine the correlation coefficient foreach time interval as well as determining the maximum and minimumrelative phase angle values and frequency values at the maximum andminimum relative phase angles for estimating the time shift error. Thecorrelation coefficients for the respective time intervals may beaveraged for comparing to the correlation threshold, for example, inblock 415. If the average correlation coefficient exceeds the thresholdas described above, then a time shift error in the synchrophasortimestamps may be detected. The error may be estimated as describedabove with respect to FIG. 8 where the difference between the maximumand minimum phase angle values and the difference between the frequencyvalues at the maximum and minimum phase angles may be determined overthe multiple time intervals over which synchrophasor measurements werecollected.

Embodiments of the inventive concept may be illustrated by way ofexample. FIGS. 9A-9C are graphical illustrations that illustrate thecorrelation between relative phase angle and frequency whensynchrophasor measurements are timestamp time shifted in a simulatedenvironment and FIGS. 10A and 10B are graphical representationsillustrating the correlation between relative phase angle and frequencywhen synchrophasor measurements are timestamped time shifted based onexperimental data obtained from a power system in accordance with someembodiments of the inventive concept. In both the simulated timestamptime shift case study and the actual timestamp time shift case study,the synchrophasor measurements were obtained from FNET/Grideye using acorrelation coefficient threshold ε of 0.95.

Simulated Synchrophasor Timestamp Time Shift Case Study

In this case study, a set of ambient data in a 200-second time window,which consists of system frequency, system angle and measured frequencyfrom a PMU at Virginia (VA), are used for timestamp time shiftdetection. A simulated data series is also added, which is generated byshifting the time of the VA PMU by 0.2 seconds. The frequency and phaseangle data is shown in FIGS. 9A and 9B, respectively, from which thetimestamp time shift may be difficult to determine. For comparison, therelative phase angle of the original PMU data and time-shifted data ofthis VA PMU are calculated and plotted in FIG. 9C. A self-normalizedseries, which is linear to the frequency of VA PMU, is added to FIG. 9Cas a curve (III) which equals to 0.2 s×360°×f(T). The curve (I) in FIG.9C shows that the normal relative phase angle varies within 1° duringthe time window while curve (II) of the time-shifted relative phaseangle has significant similarity with its frequency. The correlationcoefficient of the frequency values and time-shifted relative phaseangle values is 0.967, which exceeds the threshold for recognizing atime shift error in the PMU synchrophasor measurements. It can beobserved that the relative angle of time-shifted VA PMU (curve II)approximates to the summation of the raw relative angle (curve I) andthe frequency-linear portion (curve III), which verifies EQ. (6).

Actual Synchrophasor Timestamp Time Shift Case Study

The FNET/Grideye system has more than 100 PMUs deployed in the EasternInterconnection (EI). Two of these units, which are located in Florida(FL) and Ohio (OH), have a known timestamp time shift error of around0.9 seconds. An arbitrary 3-minute time window of ambient data is chosenin this study case to detect and calculate the time shift in thesynchrophasor timestamps.

To reduce the impact of local disturbance of individual PMUs, the systemphase angle is leveraged as the phase angle reference based on which,the relative phase angles of all PMUs are calculated. The frequency andrelative phase angle of 20 units are plotted in FIG. 10A to demonstratethe result.

Under normal operating conditions, the relative phase angles of allunits stochastically vary within ±4°, as shown in FIG. 10B. However, therelative phase angles of FL and OH units show much larger variation andsignificant similarity with frequency. The correlation coefficients ofthe two PMUs' relative angle with measured frequency are 0.975 and0.983, respectively, which strongly indicates a time shift in thetimestamped synchrophasor measurements. During the 3-minute time window,the maximum frequency deviation is 0.039 Hz, and corresponding relativephase angle deviation is 12.2°. According to EQ. (8), the estimatedtimestamp time shift is 0.87 seconds, corresponding to the known error.

Embodiments of the inventive concept may provide a methodology fordetecting a time shift in the timestamps associated with synchrophasordata provided by a PMU. Embodiments of the inventive concept may arisefrom the realization that for time shifted synchrophasor measurements,the relative phase angle and the corresponding frequency may becorrelated, e.g., by a linear relationship, and this correlation may bedetected and used as an indicator that the synchrophasor data includes atime shift error. The computational complexity of the methodology may berelatively low, which may facilitate implementation as part of a DMSincluding a phasor data concentrator module. Experiments, both simulatedand actual, demonstrate the effectiveness of the embodiments fordetecting synchrophasor measurement timestamp time shifts in a powersystem in accordance with some embodiments of the inventive concept.

Further Definitions and Embodiments

In the above-description of various embodiments of the presentdisclosure, aspects of the present disclosure may be illustrated anddescribed herein in any of a number of patentable classes or contextsincluding any new and useful process, machine, manufacture, orcomposition of matter, or any new and useful improvement thereof.Accordingly, aspects of the present disclosure may be implementedentirely hardware, entirely software (including firmware, residentsoftware, micro-code, etc.) or combining software and hardwareimplementation that may all generally be referred to herein as a“circuit,” “module,” “component,” or “system.” Furthermore, aspects ofthe present disclosure may take the form of a computer program productcomprising one or more computer readable media having computer readableprogram code embodied thereon.

Any combination of one or more computer readable media may be used. Thecomputer readable media may be a computer readable signal medium or acomputer readable storage medium. A computer readable storage medium maybe, for example, but not limited to, an electronic, magnetic, optical,electromagnetic, or semiconductor system, apparatus, or device, or anysuitable combination of the foregoing. More specific examples (anon-exhaustive list) of the computer readable storage medium wouldinclude the following: a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an appropriateoptical fiber with a repeater, a portable compact disc read-only memory(CD-ROM), an optical storage device, a magnetic storage device, or anysuitable combination of the foregoing. In the context of this document,a computer readable storage medium may be any tangible medium that cancontain, or store a program for use by or in connection with aninstruction execution system, apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device. Program codeembodied on a computer readable signal medium may be transmitted usingany appropriate medium, including but not limited to wireless, wireline,optical fiber cable, RF, etc., or any suitable combination of theforegoing.

Computer program code for carrying out operations for aspects of thepresent disclosure may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET,Python or the like, conventional procedural programming languages, suchas the “C” programming language, Visual Basic, Fortran 2003, Perl, COBOL2002, PHP, ABAP, LabVIEW, dynamic programming languages, such as Python,Ruby and Groovy, or other programming languages. The program code mayexecute entirely on the user's computer, partly on the user's computer,as a stand-alone software package, partly on the user's computer andpartly on a remote computer or entirely on the remote computer orserver. In the latter scenario, the remote computer may be connected tothe user's computer through any type of network, including a local areanetwork (LAN) or a wide area network (WAN), or the connection may bemade to an external computer (for example, through the Internet using anInternet Service Provider) or in a cloud computing environment oroffered as a service such as a Software as a Service (SaaS).

Aspects of the present disclosure are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of thedisclosure. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable instruction executionapparatus, create a mechanism for implementing the functions/actsspecified in the flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that when executed can direct a computer, otherprogrammable data processing apparatus, or other devices to function ina particular manner, such that the instructions when stored in thecomputer readable medium produce an article of manufacture includinginstructions which when executed, cause a computer to implement thefunction/act specified in the flowchart and/or block diagram block orblocks. The computer program instructions may also be loaded onto acomputer, other programmable instruction execution apparatus, or otherdevices to cause a series of operational steps to be performed on thecomputer, other programmable apparatuses or other devices to produce acomputer implemented process such that the instructions which execute onthe computer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

The flowchart and block diagrams in the figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousaspects of the present disclosure. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

The present disclosure of embodiments has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the disclosure in the form disclosed. Many variations andmodifications can be made to the embodiments without substantiallydeparting from the principles of the present invention. All suchvariations and modifications are intended to be included herein withinthe scope of the present invention.

What is claimed is:
 1. A method comprising: performing by a processor:receiving a plurality of synchrophasor measurements of a power systemsignal associated with a time interval from a phasor measurement unit(PMU), each of the plurality of synchrophasor measurements including aphase angle, frequency value, and a timestamp associated with thesynchrophasor measurement; determining a plurality of relative phaseangles based on the plurality of phase angles; determining a correlationcoefficient between the plurality of relative phase angles and aplurality of corresponding frequency values of the power system signal;detecting an error in the plurality of timestamps based on thecorrelation coefficient; estimating the error in the plurality oftimestamps based on the plurality of relative phase angles and theplurality of corresponding frequency values; adjusting the plurality oftimestamps of the plurality of synchrophasor measurements received fromthe PMU based on the error; and performing an administrative operationon the power system based on the plurality of synchrophasor measurementshaving the plurality of timestamps, respectively, that have beenadjusted responsive to the synchrophasor measurements indicating achange in a nominal frequency of the power system signal; wherein theadministration operation comprises a power system protection operation,a power system fault location operation, a power system oscillationdetection operation, or a power system event triangulation operation. 2.The method of claim 1, wherein the plurality of synchrophasormeasurements is a first plurality of synchrophasor measurements, theplurality of phase angles is a first plurality of phase angles, theplurality of timestamps is a first plurality of timestamps, and the timeinterval is a first time interval, the method further comprising:receiving a second plurality of synchrophasor measurements of the powersystem signal associated with a second time interval from the PMU, eachof the second plurality of synchrophasor measurements including a secondphase angle and a second timestamp associated with the synchrophasormeasurement; and adjusting the second plurality of timestamps associatedwith the second plurality of synchrophasor measurements received fromthe PMU based on the error.
 3. The method of claim 1, whereindetermining the plurality of relative phase angles based on theplurality of phase angles comprises: subtracting a power system averagephase angle or a phase angle of a reference PMU from each of theplurality of phase angles to obtain the plurality of relative phaseangles.
 4. The method of claim 1, wherein determining the correlationcoefficient between the plurality of relative phase angles and theplurality of corresponding frequency values of the power system signalcomprises: determining a covariance between the plurality of relativephase angles and the plurality of corresponding frequency values;determining a standard deviation of the plurality of relative phaseangles; determining a standard deviation of the plurality ofcorresponding frequency values; and dividing the covariance by a productof the standard deviation of the plurality of relative phase angles andthe standard deviation of the plurality of corresponding frequencyvalues.
 5. The method of claim 1, wherein detecting the error in theplurality of timestamps based on the correlation coefficient comprises:comparing the correlation coefficient to a threshold; and detecting theerror in the plurality of timestamps based on a difference between thecorrelation coefficient and the threshold.
 6. The method of claim 1,wherein estimating the error in the plurality of timestamps based on theplurality of relative phase angles and the plurality of correspondingfrequency values comprises: determining a relative phase angledifference between a maximum relative phase angle value of the pluralityof relative phase angles and a minimum relative phase angle value of theplurality of relative phase angles; determining a frequency differencebetween the frequency value at a time of a maximum relative phase angleand the frequency value at a time of a minimum relative phase angle; andestimating the error in the plurality of timestamps based on therelative phase angle difference divided by a product of the frequencydifference and 2π.
 7. The method of claim 1, wherein the plurality ofsynchrophasor measurements is a first plurality of synchrophasormeasurements, the plurality of phase angles is a first plurality ofphase angles, the plurality of timestamps is a first plurality oftimestamps, the time interval is a first time interval, the plurality ofrelative phase angles is a first plurality of relative phase angles, andthe correlation coefficient is a first correlation coefficient, themethod further comprising: receiving a second plurality of synchrophasormeasurements of the power system signal associated with a second timeinterval from the PMU, each of the second plurality of synchrophasormeasurements including a second phase angle and a second timestampassociated with the synchrophasor measurement; determining a secondplurality of relative phase angles based on the second plurality ofphase angles; determining a second correlation coefficient between thesecond plurality of relative phase angles and a second plurality ofcorresponding frequency values of the power system signal; anddetermining an average of the first correlation coefficient and thesecond correlation coefficient.
 8. The method of claim 7, whereindetecting the error in the first plurality of timestamps based on thecorrelation coefficient comprises: detecting the error in the firstplurality of timestamps and the second plurality of timestamps based onthe average of the first correlation coefficient and the secondcorrelation coefficient; and wherein estimating the error in the firstplurality of timestamps based on the first plurality of relative phaseangles and the first plurality of corresponding frequency valuescomprises: estimating the error in the first plurality of timestamps andthe second plurality of timestamps based on the first plurality ofrelative phase angles, the second plurality of relative phase angles,the first plurality of corresponding frequency values, and the secondplurality of corresponding frequency values.
 9. A system, comprising: aprocessor; and a memory coupled to the processor and comprising computerreadable program code embodied in the memory that is executable by theprocessor to perform operations comprising: receiving a plurality ofsynchrophasor measurements of a power system signal associated with atime interval from a phasor measurement unit (PMU), each of theplurality of synchrophasor measurements including a phase angle,frequency value, and a timestamp associated with the synchrophasormeasurement; determining a plurality of relative phase angles based onthe plurality of phase angles; determining a correlation coefficientbetween the plurality of relative phase angles and a plurality ofcorresponding frequency values of the power system signal; detecting anerror in the plurality of timestamps based on the correlationcoefficient; estimating the error in the plurality of timestamps basedon the plurality of relative phase angles and the plurality ofcorresponding frequency values; adjusting the plurality of timestamps ofthe plurality of synchrophasor measurements received from the PMU basedon the error; and performing an administrative operation on the powersystem based on the plurality of synchrophasor measurements having theplurality of timestamps, respectively, that have been adjustedresponsive to the synchrophasor measurements indicating a change in anominal frequency of the power system signal; wherein the administrationoperation comprises a power system protection operation, a power systemfault location operation, a power system oscillation detectionoperation, or a power system event triangulation operation.
 10. Thesystem of claim 9, wherein determining the correlation coefficientbetween the plurality of relative phase angles and the plurality ofcorresponding frequency values of the power system signal comprises:determining a covariance between the plurality of relative phase anglesand the plurality of corresponding frequency values; determining astandard deviation of the plurality of relative phase angles;determining a standard deviation of the plurality of correspondingfrequency values; and dividing the covariance by a product of thestandard deviation of the plurality of relative phase angles and thestandard deviation of the plurality of corresponding frequency values.11. The system of claim 9, wherein detecting the error in the pluralityof timestamps based on the correlation coefficient comprises: comparingthe correlation coefficient to a threshold; and detecting the error inthe plurality of timestamps based on a difference between thecorrelation coefficient and the threshold.
 12. The system of claim 9,wherein estimating the error in the plurality of timestamps based on theplurality of relative phase angles and the plurality of correspondingfrequency values comprises: determining a relative phase angledifference between a maximum relative phase angle value of the pluralityof relative phase angles and a minimum relative phase angle value of theplurality of relative phase angles; determining a frequency differencebetween the frequency value at a time of a maximum relative phase angleand the frequency value at a time of a minimum relative phase angle; andestimating the error in the plurality of timestamps based on therelative phase angle difference divided by a product of the frequencydifference and 2π.
 13. A computer program product, comprising: anon-transitory computer readable storage medium comprising computerreadable program code embodied in the medium that is executable by aprocessor to perform operations comprising: receiving a plurality ofsynchrophasor measurements of a power system signal associated with atime interval from a phasor measurement unit (PMU), each of theplurality of synchrophasor measurements including a phase angle,frequency value, and a timestamp associated with the synchrophasormeasurement; determining a plurality of relative phase angles based onthe plurality of phase angles; determining a correlation coefficientbetween the plurality of relative phase angles and a plurality ofcorresponding frequency values of the power system signal; detecting anerror in the plurality of timestamps based on the correlationcoefficient; estimating the error in the plurality of timestamps basedon the plurality of relative phase angles and the plurality ofcorresponding frequency values; adjusting the plurality of timestamps ofthe plurality of synchrophasor measurements received from the PMU basedon the error; and performing an administrative operation on the powersystem based on the plurality of synchrophasor measurements having theplurality of timestamps, respectively, that have been adjustedresponsive to the synchrophasor measurements indicating a change in anominal frequency of the power system signal; wherein the administrationoperation comprises a power system protection operation, a power systemfault location operation, a power system oscillation detectionoperation, or a power system event triangulation operation.
 14. Thecomputer program product of claim 13, wherein determining thecorrelation coefficient between the plurality of relative phase anglesand the plurality of corresponding frequency values of the power systemsignal comprises: determining a covariance between the plurality ofrelative phase angles and the plurality of corresponding frequencyvalues; determining a standard deviation of the plurality of relativephase angles; determining a standard deviation of the plurality ofcorresponding frequency values; and dividing the covariance by a productof the standard deviation of the plurality of relative phase angles andthe standard deviation of the plurality of corresponding frequencyvalues.
 15. The computer program product of claim 13, wherein detectingthe error in the plurality of timestamps based on the correlationcoefficient comprises: comparing the correlation coefficient to athreshold; and detecting the error in the plurality of timestamps basedon a difference between the correlation coefficient and the threshold.16. The computer program product of claim 13, wherein estimating theerror in the plurality of timestamps based on the plurality of relativephase angles and the plurality of corresponding frequency valuescomprises: determining a relative phase angle difference between amaximum relative phase angle value of the plurality of relative phaseangles and a minimum relative phase angle value of the plurality ofrelative phase angles; determining a frequency difference between thefrequency value at a time of a maximum relative phase angle and thefrequency value at a time of a minimum relative phase angle; andestimating the error in the plurality of timestamps based on therelative phase angle difference divided by a product of the frequencydifference and 2π.